A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic

Question

A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a    frictionless surface according to the graph shown above.

1) What is maximum velocity of the box?       

vmax = _____________________ m/sec

2) What is the mechanical energy of the box?       

A = ______________ J

A 3.1 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above. What is maximum velocity of the box? What is the mechanical energy of the box?

Explanation / Answer

as per the graph , distance time relation can be written as

x = -2sin(2*3.14/8 t)

thus , v= dx/dt = -3.14/2 cos (3.14/4 t)

v is maximum at x= 4 , from graph

thus Vmax = -3.14 /3 *-1 = 1.57 m/sec

mechanical energy = 1/2 m v^2 at x = 4 , as at x=4 it possase only kinetic energy

= 1/2 *3.1 *1.57*1.57 = 3.82joule

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